Do you live in Chicago? I do, and grew up here. My mom taught in CPS, and we were all sent to Catholic school. Not because the schools were better (in fact: my mom often remarked on how much lower the teacher quality was in the parochial schools, because the comp was substantially lower), but because we were Catholic, and if you don't go to Catholic K-8, you have to go to CCD. This is an extremely normal Chicago story, and not necessarily the indictment of the system you think it is.

Gates-Davis also lives on the far south side, which has structural school quality problems that aren't reasonable to pin on CTU.

I don't like CTU. I'm generally not a fan of teachers unions in major metros (most major metro teachers are in fact surprisingly well compensated). But I'm a little tired of this dunk; it's not a good one.

All that does is abandon the kids who don't get that money to a poor education.

No; the very very obvious "good thing" here would be to fix the Chicago public school system, whatever that entails. (And yes, I know that's guaranteed to be politically and logistically more difficult than just diverting more taxpayer money to private schools, but it's still the right thing to do.)